Effect-Modular Lifting of Monadic Relations

Formalize a lift of the monadic relations between base weakest- and strongest-postcondition predicate-transformer monads to the corresponding stateful monads using state monad and arrow transformers.

Background

The paper establishes the relevant monadic relations separately for the base and stateful settings. It suggests that these relations might be transported systematically through the state monad and arrow transformers, which would make the taxonomy and its relationships effect-modular rather than requiring separate proofs for each setting. This formal lifting is not developed in the paper and is explicitly deferred to future work.

References

The monadic relations are proved for the base and stateful cases separately, but we believe that a similar lift from the base to the stateful case via monad and arrow transformers, could be formalized in future work.

— A Taxonomy of Predicate Transformer Monads for Specifying Monadic Programs  (2610.23604 - Pribisova et al., 16 Oct 2026) in Section 3.2, “Monads vs. Arrows”